The ratio of the length of a tree to its shadow is $1:\frac{1}{\sqrt{3}}$. The angle of the sun's elevation is:

Let the length of the tree be $h$ and the length of its shadow be $s$.Given:
$$\frac{h}{s}=\frac{1}{\frac{1}{\sqrt{3}}}=\sqrt{3}$$
We know that $\tan \theta =\frac{\text{Height}}{\text{Shadow}}$, where $\theta$ is the angle of elevation:
$$\tan \theta =\sqrt{3}$$
$$\theta =60^{\circ }$$